Numerical Analysis of Large-Scale Sound Fields Using Iterative Methods Part I: Application of Krylov Subspace Methods to Boundary Element Analysis

Abstract

The convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3D acoustical BEM is investigated through numerical experiments. The fast multipole BEM, which is an efficient BEM based on the fast multipole method, is used for solving problems with up to about 100,000 DOF. It is verified that the convergence behavior of solvers is much affected by the formulation of the BEM (singular, hypersingular, and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCGStab2 have more stable convergence than others, and these solvers are useful when solving interior problems in basic singular formulation. When solving exterior problems with greatly complex shape in Burton-Miller formulation, all solvers hardly converge without preconditioning, whereas the convergence behavior is much improved with ILU-type preconditioning. In these cases GMRes is the fastest, whereas CGS is one of the good choices, when taken into account the difficulty of determining the timing of restart for GMRes. As for calculation for rigid thin objects in hypersingular formulation, much more rapid convergence is observed than ordinary interior/exterior problems, especially using BiCG-like solvers.

Computational Simulation in Architectural and Environmental Acoustics

“…GMRes is often referred to as a robust method, whereas it has been reported that the convergence of Restarted GMRes is greatly worse [69,70]. GMRes is often referred to as a robust method, whereas it has been reported that the convergence of Restarted GMRes is greatly worse [69,70].…”

Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method

“…A high-order Gauss-Legendre rule is used for evaluating the domain integral and the boundary integral. Finally, the complex sound pressure in the domain Ω can be computed via Equations (6) or (7) with the plane wave amplitude A l i obtained as the solution of the linear system of equations presented above.…”

“…Wave-based numerical methods, which solve a wave equation or a Helmholtz equation numerically, are physically reliable simulation methods with the capability of capturing wave phenomena such as interference and diffraction, and also of modeling boundary effects accurately by sound diffusers and sound absorbers. The finite element method (FEM) [1][2][3][4][5], boundary element method (BEM) [6], and finite difference time domain (FDTD) [7][8][9] method exemplify the often-used numerical methods for room acoustic simulations. Although they entail a huge computational effort for acoustic simulations especially at kilohertz frequencies in a real-sized room, their application to room acoustics prediction is increasing gradually by virtue of the progress of computer technology and the continuous development of efficient methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

FE/FMBE coupling to model fluid–structure interaction

“…The decrease in the number of iterations with the frequency may be attributable to the fact that at higher frequencies, the acoustic lining is more absorbent than at lower frequencies. It has been established previously (see [50,51]) that the absorption significantly affects the number of iterations. In Figure 6, the results of the numerical simulations are compared with the experimental data.…”